DOI QR코드

DOI QR Code

2022 개정 수학과 교육과정에 따른 공학 도구 활용 자료 개발 연구

Research on development of technological tool utilization materials according to the 2022 revised mathematics curriculum

  • 투고 : 2024.02.13
  • 심사 : 2024.03.14
  • 발행 : 2024.03.30

초록

본 연구는 2022 개정 수학과 교육과정이 지향하는 공학 도구 활용 교수·학습을 지원하기 위해, 수학 수업에서 활용 가능한 공학 도구를 목록화하고 관련 성취기준을 분석하여 이를 실행하는 데 필요한 교수·학습 및 평가 자료 20종을 개발하였다. 이러한 일련의 과정은 공학 도구, 수학과 교육과정, 교수·학습 및 평가를 유기적으로 연결한 목록화(List-up)-정련화(Elaboration)-개발(Development)의 LED 모형을 따라 구현하였다. 또한 본 연구는 델파이 조사, 전문가 자문, 현장 시범 적용을 추진하여 개발 자료의 타당성과 적합성을 제고하였다. 연구 결과는 공학 도구를 활용한 학생 중심 탐구 기반 수업을 설계 및 실행하고자 하는 교사, 관련된 교육 연구와 정책을 통해 수학 수업 개선을 도모하는 연구자와 정책 입안자에게 의미 있는 시사를 줄 수 있다.

This study aimed to develop teaching, learning, and assessment materials emphasizing the use of technological tools in the revised 2022 mathematics curriculum. To achieve the aim, this research reviewed previous studies to list technological tools applicable to the curriculum, analyzed achievement standards related to the use of technological tools, and developed 20 teaching, learning, and assessment materials based on these achievement standards. This process was conceptualized using the LED model, which consists of the List-up, Elaboration, and Development stages, allowing for systematic relations with technological tools, mathematics curriculum, and teaching, learning, and assessment. To ensure the quality of the developed materials, validity was secured through Delphi surveys, expert consultation, and field trials. The research findings are expected to provide assistance to teachers who aim to design and implement student-centered inquiry-based classes using technological tools, and to offer insights for developing relevant educational policies.

키워드

과제정보

이 논문은 한국과학창의재단 연구보고서 『수학 교과 공학 도구 활용 가이드 개발 연구』를 바탕으로 작성함.

참고문헌

  1. Kang, J. (2016). An analysis of generalization class using GSP for the 8th grade students in a math gifted class -Focused on Viviani theorem-. Communications of Mathematical Education, 30(1), 23-46. https://doi.org/10.7468/JKSMEE.2016.30.1.23
  2. Kang, H., & Choi, E. (2023). A study on pre-service teachers' development of digital-based teaching and learning materials of pi. Education of Primary School Mathematics, 26(1), 65-82. https://doi.org/10.7468/JKSMEC.2023.26.1.65
  3. Ko, S., Park, M., & Han, H. (2013). Teachers' perceptions on process-Focused mathematics assessment using manipulatives and technological devices. Journal of the Korean School Mathematics Society, 16(4), 675-694.
  4. Koh, E., & Han, G. (2023). The effect of the elementary school 'smart mathematics exploration team' support system on mathematical academic achievement and mathematical attitude. Journal of the Korean Association of information Education, 27(3), 235-243.
  5. Ministry of Education (1992). Mathematics curriculum (# 1992-19). Ministry of Education.
  6. Ministry of Education (2020). A comprehensive plan for mathematics education that grows together and leads the future with the power of thinking(2020~2024). SeJong: Ministry of Education.
  7. Ministry of Education (2022). Mathematics curriculum (# 2020-236 supplement 8). Ministry of Education.
  8. Ministry of Education (2022). Mathematics curriculum (# 2022-33 supplement 8). Ministry of Education.
  9. Kim, M., & Son, H. (2013). The analysis on utilization trend of the technology in secondary mathematics textbooks based on the 6th, 7th and 2007 revised curriculum in Korea. School Mathematics, 15(4), 975-994.
  10. Kim, S., Kim, M. H., Lee, I., Lee, S., & Paik, H. (2023). OECD programme for international student assessment: An analysis of PISA 2022 results. Korea Institute for Curriculum and Evaluation, Research Report RRE 2023-10.
  11. Kim, S. (2010). A study on the using of 'maths with attitude' programs in elementary. Journal of Elementary Mathematics Education in Korea, 14(1), 153-176.
  12. Kim, S. (2021). Prospective mathematics teachers' perceptions of the use of hands-on manipulatives and technological tools in teaching quadratic curves. Journal of the Korean School Mathematics Society, 24(1), 151-172. https://doi.org/10.30807/ksms.2021.24.1.008
  13. Kim, S., & Kim, H. (2019). A research on mathematics teachers' perceptions of mathematics education. The Mathematical Education, 58(3), 423-442. https://doi.org/10.7468/MATHEDU.2019.58.3.423
  14. Kim, Y., & Shin, B. (2023). An analysis of students' communication in lessons for the geometric similarity using AlgeoMath. The Korean School Mathematics Society, 26(2), 111-135.
  15. Kim, H., & Park, S. (2006). An effective approach to utilize prior studies based on using teaching tools. Communications of Mathematical Education, 20(2), 179-205.
  16. Kim, H. (2019). Computational thinking and mathematics education. Journal for Philosophy of Mathematics Education, 1(1), 17-28. https://doi.org/10.23027/JPME.2019.1.1.2
  17. Kim, H., Lee, H., Lee, H., Jin, S., Song, M., Jung, I., Cho, S., Choi, I., Choi, J., Choi, H., Hong, E., & Hong, C. (2020). AlgeoMath 3rd year development research report. Seoul: Korea Foundation for the Advancement Science & Creativity.
  18. Noh, E., & Park, J. (2019). A study on the current status of digital literacy education in secondary mathematics curriculum and lesson plan. School Mathematics, 21(3), 483-505.
  19. Park, R., Kwon, J., & Lee, D. (2019). The effects of engineering tools on students' math academic achievement and math learning attitude in middle school mathematics geometrical unit. Journal of Digital Convergence, 17(12), 67-75. https://doi.org/10.14400/JDC.2019.17.12.067
  20. Park, Y., Kim, C., Lee, C., & Kim, Y. (2020). A study on the analysis of 'organization and interpretation of data' in the mathematics textbooks for first grade in middle schools. Journal of Research in Curriculum & Instruction, 24(6), 602-615. https://doi.org/10.24231/RICI.2020.24.6.602
  21. Byun, Y., & Kim, S. (2020). TPACK analysis on self-study of high school mathematics teachers using technology. School Mathematics, 22(3), 373-394.
  22. Seo, M., & Cho, M. (2023). A study on development and effect of high school mathematics contents for artificial intelligence(AI) capability. Korean Association For Learner-Centered Curriculum And Instruction, 23(2), 771-790.
  23. Seo, H., & Lee, G. (2021). Comparative study of the effects in using geofix and cabri 3D on folding nets'activities. The Mathematical Education, 60(2), 159-172. https://doi.org/10.7468/MATHEDU.2021.60.1.159
  24. Son, H. (2011). Trend and prospect on using technology in mathematics education in Korea. School Mathematics, 13(3), 525-542.
  25. Song, C., & Lee, K. (2023). Understanding the big ideas approach to the mathematics curriculum and exploring its implementation models. The Journal of Educational Research in Mathematics, 33(1), 101-122.
  26. Yang, E., & Shin, J. (2015). A genetic decomposition of congruent transformation in dynamic geometry environments using GSP. The Journal of Educational Research in Mathematics, 25(4), 499-524.
  27. Yoo, J., Lee, J., Park, M., & Jang, H. (2020). Alternative method of irrational numbers using approximate fractions and slopes of straight lines in a spreadsheet environment. The Journal of Educational Research in Mathematics, 30(2), 353-374.
  28. Lee, K., Kim, S., Kim, N., Lee, M., Cho, S., Jee, Y., Choi, S., Na, G., Do, J., Sun, W., Lee, J., Lim, M., Choi, J., Tak, B., Rim, H., Kim, B., Na, M., Suh, B., ... Hong, Y. (2022). Research on the development policy of the 2022 revised mathematics curriculum draft (final draft). Ministry of Education, the Korea Foundation for the Advancement of Science & Creativity (KOFAC).
  29. Lee, G., Kim, D., Kim, S., Kim, H., Kim, H., Park, J., Lee, H., Lee, H., Rim, H., Jang, J., Jung, J., Cho, S., Choi, I., & Song, C. (2021). A study on the future-oriented mathematics curriculum composition for post-COVID-19. Ministry of Education.
  30. Lee, K., Jung, H., Kang, W., Ahn, B., & Baek, D. (2017). Suggestion and application of didactical principles for using mathematical teaching aids. Communications of Mathematical Education, 31(2), 203-221. https://doi.org/10.7468/JKSMEE.2017.31.2.203
  31. Lee, U., & Cho, J. (2015). Analysis of transforming mathematical representation shown in the class of composite function using the CAS. School Mathematics, 17(1), 19-33.
  32. Lee, E., & Cho, J. (2015). A study on mathematics teachers' beliefs about their use technology experiences: Focused group interviews. The Mathematical Education, 54(2), 99-117. https://doi.org/10.7468/MATHEDU.2015.54.2.99
  33. Lee, J., Lee, T., Kang, G., Kim, S., Park, H., Lee, Y., & Sim, S. (2014). A statistics education package Tong-Gramy for 5-8 graders. The Korean Journal of Applied Statistics, 27(3), 487-500. https://doi.org/10.5351/KJAS.2014.27.3.487
  34. Lee, H. (2019). Exploring the future direction of math education in AlgeoMath. East Asian Mathematical Journal, 35(4), 387-406.
  35. Yim, Y., & Hong, J. (2016). Primary students' mathematical thinking analysis of between abstraction of concrete materials and concretization of abstract concepts. School Mathematics, 18(1), 159-173.
  36. Rim, H., & Choi, I. (2019). Exploring the application of robots in mathematics classrooms based on the Van Hiele levels of development in geometry. School Mathematics, 21(4), 645-668.
  37. Jang, H., & Nam, J. (2021). The use of artificial intelligence in elementary mathematics education -Focusing on the math class support system "Knock-knock! Math Expedition"-. The Journal of Korea Elementary Education, 31(5), 105-123.
  38. Jung, S., & Park, M. (2023). Development of an artificial intelligence mathematics convergence education program tailored to elementary mathematics curriculum. Journal of Elementary Mathematics Education in Korea, 27(1), 87-108.
  39. Jung, Y. (2015). Teaching proportional reasoning in elementary school mathematics. The Journal of Educational Research in Mathematics, 25(1), 21-58.
  40. Jung, J., Park, J., Cho, H., Park, J., Jung, J., Na, M., Lee, H., Mun, J., Kim, K., Shin, S., & Park, J. (2023). Exploring the direction of the comprehensive plan for science, mathematics, information, and convergence education. Ewha Womans University Future Education Research Institute.
  41. Jung, H., & Seo, H. (2021). Analyzing how 9th grade students participate in the online mathematics lessons. School Mathematics, 23(3), 433-456.
  42. Ji, Y. (2020). Pre-service elementary teacher's statistical knowledge for teaching informal statistical inference. Doctoral dissertation, Seoul National University.
  43. Choi, G. (2022). A case study on 3D modeling of cultural assets in Korea: Focusing on the students at S gifted school. Journal of Learner-Centered Curriculum and Instruction, 22(18), 113-131.
  44. Choi, G. (2023). Development and application of teaching and learning materials for middle school quadratic functions based on smartphone activity. The Journal of Learner-Centered Curriculum and Instruction, 23(17), 251-267.
  45. Choi, J. (2023). Data analysis class plan using CODAP for middle school students. The Korean Association of Computer Education, 27(1), 18.
  46. Hong, O., Kim, J., Kim, H., Rim, Y., Kim, G., Kim, S., Kim, S., Nam, J., Shin, J., An, S., Lee, Y., Rim, M., Jung, P., & Hwang, G. (2021). A study on the development and operation of AI elementary mathematics class support system. SeJong: Ministry of Education.
  47. Whang, W., Lee, J., Kim, D., Shin, J., Lim, W., Park, J., Park, S., Baek, H., Kim, J., & Cho, S. (2015). A study on the improvement of mathematics textbooks using engineering tools. Seoul: Korea Foundation for the Advancement Science & Creativity.
  48. Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245-274.
  49. Beccuti, F., & Robutti, O. (2022). Teaching mathematics in today's society: Didactic paradigms, narratives and citizenship. For the Learning of Mathematics, 42(2), 29-34.
  50. Bhagat, K. K., & Chang, C. Y. (2015). Incorporating GeoGebra into geometry learning-A lesson from India. Eurasia Journal of Mathematics, Science and Technology Education, 11(1), 77-86.
  51. Boggan, M., Harper, S., & Whitmire, A. (2010). Using manipulatives to teach elementary mathematics. Journal of Instructional Pedagogies, 3, 1-6.
  52. Bourassa, M. (2020). TECHNOLOGY CORNER: MATHIGON. Gazette-Ontario Association for Mathematics, 58(3), 9-12.
  53. Bray, A., & Tangney, B. (2017). Technology usage in mathematics education research-A systematic review of recent trends. Computers & Education, 114, 255-273.
  54. Chalmers, C., Carter, M. L., Cooper, T., & Nason, R. (2017). Implementing "big ideas" to advance the teaching and learning of science, technology, engineering, and mathematics (STEM). International Journal of Science and Mathematics Education, 15(1), 25-43.
  55. Chechan, B., Ampadu, E., & Pears, A. (2023). Effect of using Desmos on high school students' understanding and learning of functions. Eurasia Journal of Mathematics, Science and Technology Education, 19(10), em2331.
  56. Common Core State Standards Initiative (2010). Common Core State Standards for Mathematics (CCSSM). Washington DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
  57. Dahal, N., Pant, B. P., Shrestha, I. M., & Manandhar, N. K. (2022). Use of GeoGebra in teaching and learning geometric transformation in school mathematics. International Journal of Interactive Mobile Technologies, 16(8), 65-78.
  58. Dvir, M., & Ben-Zvi, D. (2023). Fostering students' informal quantitative estimations of uncertainty through statistical modeling. Instructional Science, 51(3), 1-28.
  59. Erbas, A. K., & Yenmez, A. A. (2011). The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students' achievements in polygons. Computers & Education, 57(4), 2462-2475.
  60. Higgins, T., Mokros, J., Rubin, A., & Sagrans, J. (2023). Students' approaches to exploring relationships between categorical variables. Teaching Statistics, 45(S1), S52-S66.
  61. Hwang, G. J., & Tu, Y. F. (2021). Roles and research trends of artificial intelligence in mathematics education: A bibliometric mapping analysis and systematic review. Mathematics, 9(6), 584.
  62. Ivy, J. T., & Franz, D. P. (2013). Two classroom portraits demonstrating the interplay of secondary mathematics teachers' TPACK on their integration of the mathematical practices. In D. Polly (Ed.), Common core mathematics standards and implementing digital technologies (Chapter14). IGI Global.
  63. Korenova, L. (2017). GeoGebra in teaching of primary school mathematics. International Journal for Technology in Mathematics Education, 24(3), 155-160.
  64. Lawshe, C. H. (1975). A quantitative approach to content validity. Personnel Psychology, 28(4), 563-575. https://doi.org/10.1111/j.1744-6570.1975.tb01393.x
  65. Machado, D., Bastos, N., Hall, A., & Pais, S. (2023). Volume of geometric solids on the Desmos platform-A didactic experience in Cape Verde. European Journal of Science and Mathematics Education, 11(3), 376-391.
  66. Mollakuqe, V., Rexhepi, S., & Iseni, E. (2020). Incorporating Geogebra into teaching circle properties at high school level and it's comparison with the classical method of teaching. International Electronic Journal of Mathematics Education, 16(1), 1-11.
  67. National Council of Teachers of Mathematics (2000). Principle and standards for school mathematics. Reston, VA: Author.
  68. Nusir, S., Alsmadi, I., Al-Kabi, M., & Sharadgah, F. (2013). Studying the impact of using multimedia interactive programs on children's ability to learn basic math skills. E-learning and Digital Media, 10(3), 305-319.
  69. Pea, R. D. (1987). Cognitive technologies for mathematics education. In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 89-122). Hillsdale, NJ: Erlbaum.
  70. Phillips, A., Pane, J. F., Reumann-Moore, R., & Shenbanjo, O. (2020). Implementing an adaptive intelligent tutoring system as an instructional supplement. Educational Technology Research and Development, 68(3), 1409-1437.
  71. Reinhold, F., Hoch, S., Werner, B., Richter-Gebert, J., & Reiss, K. (2020). Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students? Learning and Instruction, 65, 101264.
  72. Saidu, S., & Bunyamin, S. (2016). Effects of geoboard and geographical globe on senior secondary school students' performance in mathematics in Kaduna State. Journal of Science, Technology & Education, 4(1), 140-148.
  73. Salinas-Herrera, J., & Salinas-Hernandez, U. (2022). Teaching and learning the notion of normal distribution using a digital resource. Canadian Journal of Science. Mathematics and Technology Education, 22(3), 576-590.
  74. Sinclair, N., & Heyd-Metzuyanim, E. (2014). Learning number with TouchCounts: The role of emotions and the body in mathematical communication. Technology. Knowledge and Learning, 19(1-2), 81-99.
  75. Sinclair, N., & Jackiw, N. (2005). Understanding and projecting ICT trends. In S. Johnston-Wilder, & D. Pimm (Eds.), Teaching secondary mathematics effectively with technology (pp. 235-252). UK: Open University Press.
  76. Singapore Ministry of Education (2020). Mathematics Syllabuses secondary one to four: Express course normal(academic) course. Curriculum Planning and Development Division of Singapore.
  77. Smith, R. C., Shin, D., & Kim, S. (2017). Prospective and current secondary mathematics teachers' criteria for evaluating mathematical cognitive technologies. International Journal of Mathematical Education in Science and Technology, 48(5), 659-681.
  78. Steenbergen-Hu, S., & Cooper, H. (2013). A meta-analysis of the effectiveness of intelligent tutoring systems on K-12 students' mathematical learning. Journal of Educational Psychology, 105(4), 970-987.
  79. Suparman, S. (2021). Is cabri 3d software effective for teaching geometry materials? A meta-analysis study in Indonesia. Journal of Advanced Sciences and Mathematics Education, 1(2), 41-51. https://doi.org/10.58524/jasme.v1i2.45
  80. Tamur, M., Juandi, D., & Kusumah, Y. S. (2020). The effectiveness of the application of mathematical software in Indonesia; A meta-analysis study. International Journal of Instruction, 13(4), 867-884.
  81. Thompson, P. W., Byerley, C., & Hatfield, N. (2013). A conceptual approach to calculus made possible by technology. Computers in the Schools, 30(1-2), 124-147.
  82. Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students' command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281-307. https://doi.org/10.1007/s10758-004-3468-5
  83. Vidergor, H. E., & Ben-Amram, P. (2020). Khan academy effectiveness: The case of math secondary students' perceptions. Computers & Education, 157, 103985.
  84. Vinner, S. (2002). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65-81). Springer.
  85. Wagner, D. (2019). Situated mathematics: Positioning mathematics ideas as human ideas. In T. Toh, & J. Yeo, (Eds.), Big ideas in mathematics: Yearbook 2019, association of mathematics educators (pp. 47-70). World Scientific.
  86. Watson, J., Fitzallen, N., Fielding-Wells, J., & Madden, S. (2018). The practice of statistics. In D. Ben-Zvi, K., Makar, & J. Gar-field (Eds.), International handbook of research in statistics education (pp. 105-138). Springer.
  87. Wozniak, F. (2017). Task design potential of using an Interactive Whiteboard for implementing inquiry-based learning in mathematics. In A. Leung, & A. Baccaglini-Frank (Eds), Digital technologies in designing mathematics education tasks: potential and pitfalls (pp. 41-54). Switzerland: Springer International Publishing.
  88. Zulnaidi, H., Oktavika, E., & Hidayat, R. (2020). Effect of use of GeoGebra on achievement of high school mathematics students. Education and Information Technologies, 25(1), 51-72.